Since streams aren’t well suited for this I suggest you collect the elements first, then do the pairwise adding in a new stream:
IntStream stream1 = IntStream.of(1, 2, 3, 4, 5);
IntStream stream2 = IntStream.of(6, 7, 8, 9, 10);
int[] arr1 = stream1.toArray();
int[] arr2 = stream2.toArray();
IntStream sumStream = IntStream.range(0, arr1.length)
.map(index -> arr1[index] + arr2[index]);
sumStream.forEach(System.out::println);
7
9
11
13
15
You want to check your assumption that there are the same number of elements in both streams, of course, and react adequately if not, may throw an exception. I’ll leave that to you.