Answer
$I_2 = 8A \\ I_8 = 2A$
Work Step by Step
First, we use Ohm's law, which states that $I=\frac{V}{R}$, to obtain:
$I_2 = \frac{V}{2} \\ I_8 = \frac{V}{8} $
We know that these two currents add to 10 Amps, so we find:
$ \frac{V}{8} + \frac{V}{2} = 10 \\ \frac{5V}{8} = 10 \\ V = 16 \ V$
Plugging this value back into the equation, we find:
$I_2 = \frac{16}{2} = \fbox{8A}\\ I_8 = \frac{16}{8} = \fbox{2A}$
