2013 AIME I Problem 3

Let ABCD be a square, and let E and F be points on \overline{AB} and \overline{BC}, respectively. The line through E parallel to \overline{BC} and the line through F parallel to \overline{AB} divide ABCD into two squares and two nonsquare rectangles. The sum of the areas of the two squares is \frac{9}{10} of the area of square ABCD. Find \frac{AE}{EB} + \frac{EB}{AE}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.