AHSME 1962 Problem 36

If both $x$ and $y$ are both integers, how many pairs of solutions are there of the equation $(x-8)(x-10) = 2^y$? $\textbf{(A)}\ 0 \textbf{(B)}\ 1 \textbf{(C)}\ 2 \textbf{(D)}\ 3 \textbf{(E)}\ \text{more than 3}$