In the question's example the b variable is not a String[] even though we casted it to E[] and defined that E is String while constructing the instance. It's an Object[]. That happens because Java doesn't know what type E is at runtime because, in this example, we didn't define a parent class for E. So, it will automatically have Object as its parent.
In other terms, public class ArrTest<E> is identical to public class ArrTest<E extends Object>.
Java doesn't know what E is at the runtime because it's unchecked. Unchecked means Java will not check if the E type is an extension or implementation of the defined parent class. So, the only thing Java knows about E at runtime is that <E extends Object>.
Therefore
E[] b = (E[]) new Object[1];
will execute as 
Object[] b = (Object[]) new Object[1];
That's why the example will not throw a ClassCastException and will confuse the developer.
If we try to use b as a real String[] then Java will throw a ClassCastException since Java sees it as an Object[]. For example, if we change the method to:
public E[] test(E a){
  E[] b = (E[])new Object[1];
  b[0] = a;
  System.out.println(b[0]);
  return b;
}
public static void main(String[] args){
    ArrTest<String> t = new ArrTest<String>();
    String[] result = t.test("Hello World");
}
Now we will receive a ClassCastException in String[] result because the returned type will be Object[] and we are trying to store it in a String[] variable. Java will see the type difference and throw the exception.
That's why casting Object[] to a generic array is discouraged, it only leads to confusion.
Before writing this answer, I created a test case with some possible ways to create a generic array and I concluded that this is the best method:
public class ExampleType<A extends Number>{
    public <T extends A> T[] bestMethod(T[] array)
    {
        if(array.length < testSize)
            array = (T[]) Array.newInstance(array.getClass().getComponentType(), testSize); //Type safety: Unchecked cast from Object to T[]
        System.out.println("in this case: "+array.getClass().getComponentType().getSimpleName());
        return array;
    }
}
It's guaranteed to return an array of the same type as the array passed as an argument and it must be an instance of A defined in the ExampleType<A extends Number>. If you create an ExampleType of Integer you will need to use an Integer[] as the argument. If you don't want an array of Integer specifically but you want to store any type of number you could use a Number[] as the argument.
If you don't need generic types in the class you could simplify it to:
public <T> T[] bestMethod(T[] array)
Of if you want it to return subclasses of Number only:
public <T extends Number> T[] bestMethod(T[] array)
Here is my test case if you want to test it yourself:
public class Test {
    public static class ArrTest<E>
    {
        public void test(E a){
            E[] b = (E[])new Object[1];
            b[0] = a;
            System.out.println(b[0]);
        }
        public E[] test2(E a){
            E[] b = (E[])new Object[1];
            b[0] = a;
            System.out.println(b[0]+" "+b.getClass().getComponentType());
            return b;
        }
        public static void main(String[] args){
            ArrTest<String> t = new ArrTest<String>();
            t.test("Hello World");
            try{String[] result = t.test2("Hello World");}catch(Exception e){System.out.println(e);}
        }
    }
    public static void main(String[] args) {
        ArrTest.main(args);
        System.out.println("#############\nWe want an array that stores only integers, sampledata: 1, samplearray: Integer");
        test(new ExampleType<Integer>(Integer.class), 1, new Integer[0], new Integer[10]);
        System.out.println("#############\nWe want an array that stores any type of Number, sampledata: 2L, samplearray: Number");
        test(new ExampleType<Number>(Number.class), 2L, new Number[0], new Number[10]);
        System.out.println("#############\nWe want an array that stores any type of CustomNumberA, sampledata: CustomB(3L), samplearray: CustomNumberA");
        test(new ExampleType<CustomNumberA>(CustomNumberA.class), new CustomNumberB(3L), new CustomNumberA[0], new CustomNumberA[10]);
        System.out.println("#############\nWe want A to be any type of number but we want to create an array of CustomNumberA, sampledata: CustomB(3L), samplearray: CustomNumberA");
        test(new ExampleType<Number>(Number.class), new CustomNumberB(3L), new CustomNumberA[0], new CustomNumberA[10]);
    }
    public static <A extends Number> void test(ExampleType<A> testType, A sampleData, A[] smallSampleArray, A[] bigSampleArray)
    {
        Class<A> clazz = testType.clazz;
        System.out.println("#############\nStarting tests with ExampleType<"+clazz.getSimpleName()+">");
        System.out.println("============\nCreating with badMethod()...");
        A[] array;
        try
        {
            array = testType.badMethod();
            testType.executeTests(array);
        }
        catch(Exception e){ System.out.println(">> ERR: "+e); }
        System.out.println("============\nCreating with alsoBadMethod("+sampleData+" ["+sampleData.getClass().getSimpleName()+"])...");
        try
        {
            array = testType.alsoBadMethod(sampleData);
            testType.executeTests(array);
        }
        catch(Exception e){ System.out.println(">> ERR: "+e); }
        System.out.println("============\nCreating with nearlyGoodMethod("+smallSampleArray.getClass().getSimpleName()+" len: "+smallSampleArray.length+")...");
        try
        {
            array = testType.nearlyGoodMethod(smallSampleArray);
            testType.executeTests(array);
        }
        catch(Exception e){ System.out.println(">> ERR: "+e); }
        System.out.println("============\nCreating with nearlyGoodMethod("+bigSampleArray.getClass().getSimpleName()+" len: "+bigSampleArray.length+")...");
        try
        {
            array = testType.nearlyGoodMethod(bigSampleArray);
            testType.executeTests(array);
        }
        catch(Exception e){ System.out.println(">> ERR: "+e); }
        System.out.println("============\nCreating with bestMethod("+smallSampleArray.getClass().getSimpleName()+" len: "+smallSampleArray.length+")...");
        try
        {
            array = testType.bestMethod(smallSampleArray);
            testType.executeTests(array);
        }
        catch(Exception e){ System.out.println(">> ERR: "+e); }
        System.out.println("============\nCreating with bestMethod("+bigSampleArray.getClass().getSimpleName()+" len: "+bigSampleArray.length+")...");
        try
        {
            array = testType.bestMethod(bigSampleArray);
            testType.executeTests(array);
        }
        catch(Exception e){ System.out.println(">> ERR: "+e); }
    }
    @RequiredArgsConstructor @ToString()
    public static class CustomNumberA extends Number{
        @Delegate final Long n;
    }
    public static class CustomNumberB extends CustomNumberA{
        public CustomNumberB(Long n) { super(n); }
    }
    @RequiredArgsConstructor
    public static class ExampleType<A>{
        private int testSize = 7;
        final Class<A> clazz;
        public A[] badMethod()
        {
            System.out.println("This will throw a ClassCastException when trying to return the array because Object is not a type of "+clazz.getSimpleName());
            A[] array = (A[]) new Object[testSize]; //Warning: Type safety: Unchecked cast from Object[] to A[]
            System.out.println("Array of "+array.getClass().getComponentType()+" created");
            return array;
        }
        public A[] alsoBadMethod(A sampleType)
        {
            System.out.println("Will not respect A type ("+clazz.getSimpleName()+"), will always use the highest type in sampleType and tell that it's A[] but it's not, in this case will return "+sampleType.getClass().getSimpleName()+"[] and said it was "+clazz.getSimpleName()+"[] while developing");
            A[] array = (A[]) Array.newInstance(sampleType.getClass(), testSize); //Type safety: Unchecked cast from Object to A[]
            return array;
        }
        public A[] nearlyGoodMethod(A[] array)
        {
            System.out.println("The only guarantee is that the returned array will be of something that extends A ("+clazz.getSimpleName()+") so the returned type is not clear, may be of A or of the type passed in the argument but will tell it's A[] but may not be");
            if(array.length < testSize)
                array = (A[]) Array.newInstance(array.getClass().getComponentType(), testSize); //Type safety: Unchecked cast from Object to A[]
            System.out.println("in this case: "+array.getClass().getComponentType().getSimpleName()+"[], expecting: "+clazz.getSimpleName()+"[]");
            return array;
        }
        public <T extends A> T[] bestMethod(T[] array)
        {
            System.out.println("It's guaranteed to return on array of the same type as the sample array and it must be an instance of A, so, this is the best method");
            if(array.length < testSize)
                array = (T[]) Array.newInstance(array.getClass().getComponentType(), testSize); //Type safety: Unchecked cast from Object to T[]
            System.out.println("in this case: "+array.getClass().getComponentType().getSimpleName()+"[], expecting: "+array.getClass().getComponentType().getSimpleName()+"[]");
            return array;
        }
        public void executeTests(A[] array)
        {
            tryToSet(array, 0, 1);
            tryToSet(array, 1, 2L);
            tryToSet(array, 2, 3.1);
            tryToSet(array, 3, 4F);
            tryToSet(array, 4, (byte)0x5);
            tryToSet(array, 5, new CustomNumberA(6L));
            tryToSet(array, 6, new CustomNumberB(7L));
        }
        public void tryToSet(A[] array, int index, Object value)
        {
            System.out.println("Trying to set "+value+" ("+value.getClass().getSimpleName()+") at "+index+" in a array of "+array.getClass().getComponentType().getSimpleName());
            try
            {
                if(array instanceof Object[]) ((Object[]) array)[index] = value;
                else array[index] = (A) value; //Type safety: Unchecked cast from Object to A
                System.out.println("## OK: Success: "+array.getClass().getComponentType().getSimpleName()+"["+index+"] = "+array[index]);
            }
            catch(Exception e){ System.out.println(">> ERR: "+e); }
        }
    }
}
And here are the test results... You can see that the bestMethod always returns the expected result.
http://pastebin.com/CxBSHaYm