Goal Seek can only handle one "target" cell, so you need to change the problem to a single target cell. Again, start with some algebra for a system of equations:

21.6-0.05*D10=0.1*E10+0.25*F10
185-D10=E10+F10

Assign any suitable number to D10.

Solve both equations for E10
Set the resulting equations equal to each other
Have Goal Seek solve this equation for F10
Use the resulting value for F10 to find E10.