2005 AMC 10B Problem 24

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

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