Solve for r:
E/e = (r + R)/(R - r)
E/e = (r + R)/(R - r) is equivalent to (r + R)/(R - r) = E/e:
(r + R)/(R - r) = E/e
Cross multiply:
e (r + R) = E (R - r)
Expand out terms of the left hand side:
e r + e R = E (R - r)
Expand out terms of the right hand side:
e r + e R = E R - E r
Subtract e R - E r from both sides:
r (E + e) = E R - e R
Divide both sides by E + e:
Answer: | r = (E R - e R)/(E + e)=R[E - e] / [E + e]