AHSME 1961 Problem 33

The number of solutions of $2^{2x}-3^{2y}=55$, in which $x$ and $y$ are integers, is: $$\textbf{(A)} \ 0 \textbf{(B)} \ 1 \textbf{(C)} \ 2 \textbf{(D)} \ 3 \textbf{(E)} \ \text{More than three, but finite}$$