Finding an unknown resistance with superposition
With superposition just write three components of I1 (say I1.1(R2), I1.2(R2) and I1.3(R2) ) each with one single source activated. 

Each expression will be function of unknown R2.  Then you sum them up and finally solve this to be 10mA. 

I2 will automatically be 10mA too for a simple KCL at center node.  

Alternatively Ohm's law would solve this right away:

Given I1=10mA Ux at center node will be \$U_\text{x}=U_1-R_1I_1=6.53\,\text{V}-458\,\Omega\times10\,\text{mA}=1.95\,\text{V}\$

On the other hand
$$I_2=\frac{U_2-U_\text{x}}{R_2+R_\text{i}}
\quad\Rightarrow\quad
R_2=\frac{U_2-U_\text{x}}{I_2}-R_\text{i}=\frac{8.5\,\text{V}-1.95\,\text{V}}{10\,\text{mA}}-0.4\,\Omega\approx 655\,\Omega$$