In triangle \( \triangle ABC\), \(AB=30 \) and \( AC=28 \). Point \( D \) lies on line segment \( AB \) such that \( BD=16 \) and point \( E \) lies on line segment \( AC \) such that the area of quadrilateral \( BCED \) is \( \frac{7}{10} \)th of the area of triangle \( \triangle ABC \). Find the length of \( AE \).

This problem is posed by Minimario M.

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