AMC 12 2005b 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 $x+y+m$?

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