2017 Fermat Problem 21

In the sum shown, each letter represents a different digit with T \neq 0 and W \neq 0. How many different values of U are possible?

\begin{array}{cccccc} & & W & X & Y & Z \\ + & & W & X & Y & Z \\ \hline & T & W & U & Y & V \\ \end{array}

\textbf{(A)}\ 1\quad \textbf{(B)}\ 2\quad \textbf{(C)}\ 3\quad \textbf{(D)}\ 4\quad \textbf{(E)}\ 5

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.