Let $ABC$ be a triangle with $m(\widehat{ABC}) = 90^{\circ}$. The circle with diameter $AB$ intersects the side $[AC]$ at $D$. The tangent to the circle at $D$ meets $BC$ at $E$. If $|EC| =2$, then what is $|AC|^2 - |AE|^2$ ?

$\textbf{(A)}\ 18 \qquad\textbf{(B)}\ 16 \qquad\textbf{(C)}\ 12 \qquad\textbf{(E)}\ 10 \qquad\textbf{(E)}\ \text{None}$