Exploit the interchangeability of x and y by splitting the sum evenly: set x = 10 + r and y = 10 − r. Substituting into the product gives (10 + r)(10 − r) = 34, so 100 − r^2 = 34 and r^2 = 66. Taking square roots yields r = ±sqrt(66). Therefore, the solutions are (x, y) = (10 + sqrt(66), 10 − sqrt(66)) and (10 − sqrt(66), 10 + sqrt(66)).