Find out in linear time whether there is a pair in sorted vector that adds up to certain value

Given an std::vector of distinct elements sorted in ascending order, I want to develop an algorithm that determines whether there are two elements in the collection whose sum is a certain value, sum.

I've tried two different approaches:

1. I can scan the whole vector and, for each element in the vector, apply binary search (std::lower_bound) on the vector for searching an element corresponding to the difference between sum and the current element. This is an O(n log n) time solution that requires no additional space.

2. I can traverse the whole vector and populate an std::unordered_set. Then, I scan the vector and, for each element, I look up in the std::unordered_set for the difference between sum and the current element. Since searching on a hash table runs in constant time on average, this solution runs in linear time. However, this solution requires additional linear space because of the std::unordered_set data structure.

Nevertheless, I'm looking for a solution that runs in linear time and requires no additional linear space. Any ideas? It seems that I'm forced to trade speed for space.