Let $X$ and $Y$ be two independent standard Normal variables. Let $M := \max(X, Y)$ and $L := \min(X, Y)$. It is given that the covariance between $M$ and $L$ is given by $\text{Cov}(M, L) = 1 / \pi$ How do I find the variance of $M$ and $L$?

We first note that $M - L = |X - Y|$ and $M + L = X + Y$. Since $X$ and $Y$ are independent we have $X + Y \sim \mathcal{N}(0, 2)$. Therefore $\text{Var}(X + Y) = 2 = \text{Var}(M) + \text{Var}(L) + 2 \text{Cov}(M, L)$. Hence $\text{Var}(M) + \text{Var}(L) + \frac{2}{\pi} = 2$.

I could not find another equation involving $\text{Var}(M)$ and $\text{Var}(L)$ using $M - L = |X - Y|$, as I could not find the variance of $|X - Y|$. How do I continue from this point? Also,are there any other approaches which use the symmetry property of the standard normals?