2003 AMC 8 Problem 14

In this addition problem, each letter stands for a different digit.

\begin{array}{cccc}&T & W & O\\ + &T & W & O\\ F& O & U & R\end{array}

If T = 7 and the letter O represents an even number, what is the only possible value for W?

\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2\qquad \textbf{(D)}\ 3\qquad \textbf{(E)}\ 4

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