Let A B C D be a square, and let E and F be points on \overline{A B} and \overline{B C}, respectively. The line through E parallel to \overline{B C} and the line through F parallel to \overline{A B} divide A B C D 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 A B C D. Find \frac{A E}{E B}+\frac{E B}{A E}.