Solving Linear Equations System in Matrix form with unknowns on both sides

I have the system of equations in the form of k.u=f where k is n by n matrix and both u and f are n by 1 vectors. The problem is that I have unknowns on both u and f vectors and I want to solve the system for these unknowns. Any ideas how to do that?

[madhan ravi]

Can you upload the known datas ?

[Morteza Ghafoori]

It's actually a code that gets info by inputs and then solves the system so no definite data is given

[Torsten]

But the total number of unknowns is equal to n ?

[Morteza Ghafoori]

the maximum number of unknowns is n but it can be less than that (depends on the input)