Do you know how to solve a system of one quadratic and one linear equation?

Geometry Level 3

The hypotenuse of the right-angled triangle \(ABC\) has length \(AB=c=35\). The square \(CDEF\), whose side length is \(d=12\), is inscribed in the triangle as shown above (pictured red).

If \(AC=b\) is the longer leg of the triangle, and \(BC=a\) is the shorter leg, find the value of \(b-a\).

Hint: \( \triangle ABC \sim \triangle EBF \).

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