Let $T$(Talent Distribution) and $E$(Environment) be independently and uniformly distributed random variables over the interval [0,1] and [0,$c_1$] respectively. Considering $c_1>1$, I have now found out a distribution for $X_A=T+E$ for which I followed this blog:
$f_{X_A}(x){}={\bf{1}}_{\left\{0\le x \le 1\right\}}\dfrac{z}{c_1} +{\bf{1}}_{\left\{1 < z \le c_1\right\}} {}+{}{\bf{1}}_{\left\{c_1 < z \le c_1+1\right\}}\dfrac{c_1+1-z}{c_1}\,.$
Similarly, if we consider another distribution $X_B=T+E'$ where $E'$ is uniformly distributed between $[0,c_2]$ such that:
$f_{X_B}(x){}={\bf{1}}_{\left\{0\le x \le 1\right\}}\dfrac{z}{c_2} +{\bf{1}}_{\left\{1 < z \le c_2\right\}} {}+{}{\bf{1}}_{\left\{c_2 < z \le c_2+1\right\}}\dfrac{c_2+1-z}{c_2}\,.$
Then I am interested in finding the PDF for $X_A-X_B$.
Being new to probability distributions, I find it hard to compute it easily. Any thoughts appreciated.