Check out the syntax for Function. I would try with Solve:
With[{k1 = 5, b = 2}, Solve[y == 1 - Sum[a^k/k! Exp[-a], {k, 0, Infinity}] Sum[ 1/n! Exp[b x] (b x)^n, {n, 0, k1}], x]]
but it seems too hard.
