Differences in Medians

As $\bigtriangleup ABD$ is a right triangle, it can be inscribed in a semicircle with its hypotenuse $\overline{AB}$ as its diameter and $D$ on the circumference of the corresponding circumscribing circle. Likewise for $\bigtriangleup ABE$ , which shares a hypotenuse, and hence a circumscribing circle, with point $E$ on its circumference. Point $C$ is therefore the center of the corresponding circle and points $D$ and $E$ are on the circle, thus $\overline{CD}$ and $\overline{CE}$ are both radii of the circle with center $C$ . Therefore these segments are congruent, giving $\overline{CD} - \overline{CE} = \boxed{0}$ .