Answer
$r=\frac{eR}{E-e}$
Work Step by Step
Use the rule $\frac{a}{b}=\frac{c}{d} \longrightarrow ad=bc$ to obtain:
$$E\cdot r=e(R+r)
\\Er=eR+er$$
Subtract $er$ from both sides:
$$Er-er = eR$$
Factor out $r$:
$$r(E-e)=eR$$
Divide $E-e$ to both sides:
$$\frac{r(E-e)}{E-e}=\frac{eR}{E-e}
\\r=\frac{eR}{E-e}$$
