A positive integer n is called squareful if p | n implies p^2 | n for all primes p. Erdos asked for estimates of the number V(x) of integers not exceeding x that can be written as a sum of two squareful numbers. In this talk, we shall present the result V(x) = x (\log x)^{-\alpha +o(1)} with alpha = 1 - 2^{-1/3} = 0.206.... The proof based on new developments in theory of binary quadratic forms.