Answer
$r=\frac{nE-RI}{nI}$
Work Step by Step
Multiply $R+nr$ to both sides of the equation:
$$\require{cancel}
(R+nr) \cdot I=(R+nr)\cdot \frac{nE}{R+nr}
\\(R+nr) \cdot I=\cancel{(R+nr)}\cdot \frac{nE}{\cancel{R+nr}}
\\RI+nrI=nE$$
Subtract $RI$ to both sides:
$$RI+nrI-RI=nE-RI
\\nrI=nE-RI$$
Divide $(nI)$ to both sides:
$$\frac{nrI}{nI}=\frac{nE-RI}{nI}
\\r=\frac{nE-RI}{nI}$$
