An isosceles right triangle $$ABC$$ has legs $$AC=BC=10$$. A point $$D$$ is chosen on $$AC$$ such that $$\tan{\angle{ABD}}=\frac{1}{5}$$. Then length of $$AD$$ is $$\frac{a}{b}$$ for relatively prime $$a$$ and $$b$$. Find $$a-b$$.