Assume $X_1$ and $X_2 \sim N(0,1)$ independent and identically distributed random variables. Determine the distribution of $T_3=\frac{(X_2+X_1)^2}{\sqrt{(X_2-X_1)^2}}$
We know $(\frac{X_2+X_1} {\sqrt{2}})^2 \sim \chi^2_{(1)}$, the same for $(\frac{X_2-X_1} {\sqrt{2}})^2 \sim \chi^2_{(1)}$.
My problem is that I don´t know how to handle the square root, I think the distribution looks like a Student´s T or an F one. How can I proceed?