Triangle Trigonometry and Vectors · Challenge problem

Vectors $\mathbf{u}$ and $\mathbf{v}$ satisfy $\|\mathbf{u}\|=3$, $\|\mathbf{v}\|=5$, and $\|\mathbf{u}+\mathbf{v}\|=7$. Find $\|\mathbf{u}-\mathbf{v}\|$.