Let \triangle A B C be a right triangle with A B=4, B C=5, and hypotenuse A C. Let I be the incenter of \triangle A B C and E be the excenter of \triangle A B C opposite A (the center of the circle tangent to B C and the extensions of segments A B and A C). Suppose the circle with diameter I E intersects line A B beyond B at D. If B D=\sqrt{a}-b, where a and b are positive integers. Find a+b.