Question: Solve can't find analytically solution... but I can?

Hi Maple-Prime-ers!

I have a system of equations, containing 18 variables and 13 equations, making this a 5 degree of freedom (DOF) system.  I would like to analytically solve each of the equations in terms of each of these DOFs.  Normally I would use solve(system, dof_variables) to accomplish this, but it doesn't return anything.  Not even [].

I can solve this system by hand.  I've included a hand-solution involving isolate() and subs() in the attached worksheet.  I'm looking to incorporate this in an optimization algorithm with varying system, so I would like an automated way of doing this.

Does anybody have any suggestions to get solve to work as intended?

3driversys_FD_BRAKE_ICE_GEN.mw

Here is the system I am talking about:

The free variables are:  {FD_T, FD_W, ICE_T, EM2_T, BRAKE_T}

I'm looking for a solution in this form: