AE is 25. AE (or ADE) is comprised of AD and DE. You found AE (which was asked). AD = 4 and DE = 21.
Good!
Actually, the correct set up is this: If two secants intersect at an external point, the product of the external segment of one secant times the whole secant is equal to the external part of the other secant times the whole secant.
In other words, by my diagram:
Therefore,