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Problem Description Quadrilateral \(ABCD\) satisfies \(\angle ABC = \angle ACD = 90^{\circ}, AC = 20\), and \(CD = 30\). Diagonals \(\overline{AC}\) and \(\overline{BD}\) intersect at point \(E\), and \(AE = 5\). What is the area of quadrilateral \(ABCD\)? $$\textbf{(A) } 330 \qquad\textbf{(B) } 340 \qquad\textbf{(C) } 350 \qquad\textbf{(D) } 360 \qquad\textbf{(E) } 370$$

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