Finding numbers from quotient of sums with roots.

Question

If $$\frac{\sum_{n=1}^{99} (\sqrt{10} + \sqrt{n})}{\sum_{n=1}^{99} (\sqrt{10} - \sqrt{n})} = a + \sqrt{b}$$ where $a$ and $b$ are integers , find the value of $a^2 + b^2$.