explanation of solution

The solution seems to be the the following, but I need a more in-depth explanation, particularly on why we should use merge sort and binary sort.

Here is the problem at a high level (you can look at the attachment for more detail):
Describe a (n log_2 n) time algorithm that, given a set S of n real numbers
and another real number x, determines whether or not there exist two
elements in S whose sum is exactly x.


Solution:
Sort the array using an algorithm of order O(n log n) (You can use mergesort but
you cannot use quicksort)
Then for every element y in the array binary search the sorted array for x - y

O(n log n) + O(n log n) = O(n log n)