Trigonometry · Superchallenge problem

A parallelogram is spanned by vectors $\mathbf u$ and $\mathbf v$ with $|\mathbf u| = 5$. Its diagonals have lengths $|\mathbf u + \mathbf v| = 8$ and $|\mathbf u - \mathbf v| = 6$. Find the cosine of the angle between $\mathbf u$ and $\mathbf v$.