Question 1023114
Assume you mean

{{{1 = E - e/(R+r)}}} 
Rearrange to
E - 1 = {{{e/(R+r)}}} 
multiply both sides by (R+r)
(R+r)(E-1) = e
FOIL
RE - R + rE - r = e
Subtract RE and Add R to both sides
rE - r = e - RE + R
factor out r
r(E-1) = e - RE + R
Divide both sides by (E-1)
r = {{{(e-RE+R)/(E-1)}}}