Finding an element without pair in a list O(n**2)
This is not a review, but an extended comment.
The linear time/constant space solution is too well known to be spelled out again. However, here it goes.
XOR of two equal numbers is 0, and XOR of a number and 0 leaves the number unchanged. XOR is commutative and associative operation; we may perform it in any order we wish, and arrive to the same result. In other words, if we XOR all of them, each pair of numbers would cancel to 0, and the final result would be the number without a pair, the one we are looking for.