Breaking RSA

Eve is not convinced she needs to factor N = pq in order to break RSA. She argues: "All I need to know is (p−1)(q−1)... then I can find d as the inverse of e mod (p−1)(q−1). This should be easier than factoring N." Prove Eve wrong, by showing that if she knows (p−1)(q−1), she can easily factor N (thus showing finding (p − 1)(q − 1) is at least as hard as factoring N). Assume Eve has a friend Wolfram, who can easily return the roots of polynomials over R (this is, in fact, easy).