Question

in the diagram, AE is tangent to the circle at point a and secant DE intersects the circle at point C and D. the iines intersect outside of the circle at point E

Answer 1

Recall the secant-tangent theorem, and you have
EA^2 = EC*CD
12^2 = 8*(x+10)
and now ED = EC+CD = 8+x+10

I suspect a typo somewhere in the murk above