probability - distribution function of the difference of two correlated chi-squared variables

I am trying to get the probability distribution function of the difference of two correlated chi-squared variable, $Z=X−Y.$ Given that $f_X(x)$ and $f_Y(y)$ are known, and both variables are chi-squaree distributed. $X$ and $Y$ have the same degree of freedom. lets assume that the mean and variance values for $X$ and $Y$ are $\mu_x, \sigma^2_x$ and $\mu_y$ and $\sigma_y^2,$ respectively. the covariance between $X$ and $Y$ is $\sigma_{xy}.$ So how can I calculate the variance and distribution of $Z$ ($f_Z(z)$). what if $\sigma_y^2= \sigma_x^2$?