How does size of a number in an array affect time complexity algorithm analysis?
Actually, you can avoid any higher precision calculations. 

Assume you are adding n k-bit numbers in one array, and adding n+1 k-bit numbers in the other array. The difference is a k-bit number (the one extra number that was added to the other array). 

So you can perform the addition, and just ignore anything beyond k bits. Instead of getting the sum, you get the sum modulo $2^k$, but that is enough to get the correct result.