Denote the first angle as x and second as y (degrees). Complementary angles mean x + y = 90. "One angle is 18 degrees more than two times the other angle" translates to x = 18 + 2*y.

Substitute this to the first equation we obtain 18 + 3y = 90, 3y = 72, y = 24. So x = 18 + 2y = 66.

Answer: one angle is 24 degree and another is 66 degree.