Well, you cannot search in the Stream as long as Stream is an unfinished set of pipelines, i.e. operations. It makes no sense to compare it with such Stream.
The next thing that seems odd to me is probably a typo. I assume you want to search in the stream1 instead of stream2, hence:
stream2 = stream2.filter(e -> stream1.contains(e));
The only way is to compare a LongStream with a collection which is optimized for such search. I assume you want to continue the stream1 after you perform the search, so perform these steps:
- Close 
stream1 converting it to a List<Long> list1. 
- Perform the search in 
stream2 using list1 from stream1. 
- Open 
stream1 again for further processing. 
LongStream stream1 = ...
LongStream stream2 = ...
List<Long> list1 = stream1.boxed()                       // list1 from stream1 ..
                          .collect(Collectors.toList()); // .. which also closes stream1
stream2  = stream2.filter(list1::contains);              // perform search
stream1 = list1.stream().mapToLong(l -> l);              // open stream1 as LongStream
Edit: Use Set for better performance as @fps suggests in his answer.