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Rearrange to
E - 1 =
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 =