$\frac{{{i_1}}}{{{i_2}}} = \frac{9}{{18}} = \frac{1}{2}$
and $i = {i_1} + {i_2}$

$ \Rightarrow \frac{i}{{{i_1}}} = 1 + \frac{{{i_2}}}{{{i_1}}} = 1 + 2 = 3$

From $P = {i^2}R \Rightarrow \frac{{{P_{10\,\Omega }}}}{{{P_{18\,\Omega }}}} = {\left( {\frac{i}{{{i_1}}}} \right)^2} \times \frac{{10}}{{18}}$ $ \Rightarrow {P_{10\,\Omega }}\, = 10\,W$