Can anyone solve this?
Sub test
Dim i as integer
For I = 1 to 10
   ActiveCell.Offset(0, 2).Formula = "=Sum(E15,&i&)"
Next I
End Sub
your actual goal is unclear
you may want to start form this code
Sub test()
    Dim i As Integer
    For i = 1 To 10
       cells(i, 4).Formula = "=Sum(E" & i & ":E15)"
    Next
End Sub
and adjust it to your needs, knowing that:
it currently writes in cells "D1:D10"
since cells(i, 4)  references a cell in 4th column (i.e.: column "D") 4 and i row, and we're inside a loop where i is looping through 1 to 10
so if:
you want to reference a different column then just change 4 to the proper column index 
you want to reference a different row then just change i to the proper row index (may be some i+2 if you need to iterate through 1 to 10 but start writing from row 3)
the formula written in those cells is:
=SUM(E1:E15) in D1,
=SUM(E2:E15) in D2,
....
=SUM(E10:E15) in D10.
so just change "=Sum(E" & i & ":E15)" to your actual needs
You're close, trying to use ampersands (&) to concatenate strings.
ActiveCell.Offset(0, 2).Formula = "=Sum(E15," & i & ")"
Use the ampersands between strings to merge them, not inside strings.