In the overlapping triangles $△ABC$ and $△ABE$ sharing common side $AB$, $\angle EAB$ and $\angle ABC$ are right angles, $AB=8$, $BC=12$, $AE=15$, and $\overline{AC}$ and $\overline{BE}$ intersect at $D$. What is the difference between the areas of $△ADE$ and $△BDC$?