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:
$$\frac{R(E-e)}{E-e}=\frac{er}{E-e}
\\R=\frac{er}{E-e}$$