Sum of 2 exponential distribution with different parameters

Question

Let $X\sim Exp(\lambda_1)$ and $Y\sim Exp(\lambda_2)$, I am trying to find the distribution of $Z = X+Y$. I understand that $f_z(z)=\frac{\lambda_1 \lambda_2}{\lambda_2-\lambda_1} \left(\exp[-\lambda_1 z] - \exp[-\lambda_2 z]\right)$, but I am struggling with mapping this back to a distribution.