A value of $x$ satisfying the equation $x^2 + b^2 = (a - x)^2$ is:
$\textbf{(A)}\ \frac{b^2 + a^2}{2a}\qquad  \textbf{(B)}\ \frac{b^2 - a^2}{2a}\qquad  \textbf{(C)}\ \frac{a^2 - b^2}{2a}\qquad  \textbf{(D)}\ \frac{a - b}{2}\qquad  \textbf{(E)}\ \frac{a^2 - b^2}{2}$
Solve for x:
\[x^2+b^2=(a-x)^2\]
\[x^2+b^2=x^2-2ax+a^2\]
\[b^2=-2ax+a^2\]
\[2ax=a^2-b^2\]
\[x=\frac{a^2-b^2}{2a} \to \boxed{\text{(C)}}\]