negative voltage of a differential amplifier
You only need VEE to be a negative voltage if you want the outputs to be able to swing around 0 V.
If you power the circuit from a single supply with VEE at 0 V then it should be fairly obvious that V1out and V2out cannot get down to 0 V as there will be a voltage drop across the transistor CE and REM. That means that your output voltages will be restricted to somewhere around mid-supply. This might be OK in some applications.
If, on the other hand, you make VEE a negative voltage with respect to circuit ground then your inputs and outputs can swing either side of zero. This may be a critical requirement in other applications.