2005 AMC 12B Problem 19

Let x and y be two-digit integers such that y is obtained by reversing the digits of x. The integers x and y satisfy x^{2}-y^{2}=m^{2} for some positive integer m. What is x+y+m?

\mathrm{(A)}\ 88 \qquad \mathrm{(B)}\ 112 \qquad \mathrm{(C)}\ 116 \qquad \mathrm{(D)}\ 144 \qquad \mathrm{(E)}\ 154 \qquad

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