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Geometry Level 3

Let \(ABCD\) be a square, and let \(E\) and \(F\) be points on \(AB\) and \(BC,\) respectively. The line through \(E\) parallel to \(BC\) and the line through \(F\) parallel to \(AB\) divide \(ABCD\) into two squares and two non-square rectangles. The sum of the areas of the two squares is \(\frac{9}{10}\) of the area of square \(ABCD.\)

Find \(\frac{AE}{EB}+\frac{EB}{AE}.\)