To answer your question , you just have to remember that
A XOR B = C => C XOR A = B
and it immediately follows that
(PARTIAL SUM) XOR (MISSING ELEMENT) = (TOTAL) =>
(TOTAL) XOR ( PATIAL SUM) = (MISSING ELEMNT)
To prove the first property, just write down the XOR truth table:
A B | A XOR B
0 0 | 0
0 1 | 1
1 0 | 1
1 1 | 0
Truth table in short : if both the bits are same, result of XOR is false, true otherwise.
On an unrelated note, this property of XOR makes it a nice candidate for simple ( but not trivial ) forms of encryption.
