+1678 Let $A$, $B$, $C$, $D$, and $E$ be points in the plane such that:
* $D$ is on line $AE$ with $\overline{CD} \perp \overline{AE}$.
* $B$ is on line $CE$ with $\overline{AB} \perp \overline{CE}$.
* $AB = 4$, $BE = 3$, and $CE = 8$.
Find the length $DE$.
