1962 AHSME 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 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2 \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ \text{more than 3}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.