I get this for the case where V1 and V2 are floating (i.e., a voltage is a applied between them that is not ground references). It has the same problem in that the actual output voltages are not uniquely defined, just the difference. Also, if there is ANY common mode path at the inputs, then this solution no longer applies.Rather curiously, I have ...
\( V_{o1} - V_{o2 }=(V_2-V_1) \frac{(R_2+R_4)}{(R_1+R_3)}\)
.....????