Foundations · Superchallenge problem

The digits $a$ and $b$ make the repeating decimals $0.\overline{ab} = 0.ababab\ldots$ and $0.\overline{ba} = 0.bababa\ldots$. Their sum is $\dfrac{4}{3}$ and their difference $0.\overline{ab} - 0.\overline{ba}$ is $\dfrac{2}{11}$. What is the two-digit number $\overline{ab}$ (that is, $10a + b$)?