Well, you could "brute force" it.

You can find angles BAC and BCA since you know the sides of triangle ABC. From angle BAC you can find its supplement CAE. And CAE is split into two equal parts: CAE and EAD. So you have angle CAD. You can also find the supplement to angle BCA. Then you have two angles and a side of triangle ACD. Now go from there.

It sounds worse than it is....

-Dan