When you subtracted, What you did here was you found the separation between the thief and the policeman in the LHS, and in the RHS you found the relative speed between them, as you only subtracted the velocities since t is common. Thus it is the alternate method TKA suggested.
When you add the equations we get 100=19t which is the time taken by something with a speed 9m19m/s to travel 100m which does not really help solve the question.