A Tricky Trapezoid

Note that $\angle ADC + \angle DCB = 270 \rightarrow \angle BAD + \angle CBA = 90.$ This means that we can extend $AD$ and $BC$ to form a right triangle.

Now, it is clear that the medians of $\bigtriangleup DEC$ and $\bigtriangleup AEB$ lie on the same line. Thus the answer is $\frac{24}{2}$ - $\frac{14}{2}$ = 5.