Answer
$R = 8.0~\Omega$
Work Step by Step
When the resistance is $R$:
$\mathscr{E} = i~R = (5.0~A)~R$
When the resistance is $R+2.0~\Omega$:
$\mathscr{E} = (4.0~A)~(R+2.0~\Omega)$
We can find $R$:
$(5.0~A)~R = (4.0~A)~(R+2.0~\Omega)$
$(1.0~A)~R = (4.0~A)~(2.0~\Omega)$
$R = 8.0~\Omega$
