Welcome to Physics SE. You should give a little more detail about your circuit and what you are trying to achieve using it.
So the purpose of this experiment to find the null point that is when there is no current passing through the Galvanometer and compare the emf of the two cells.
If $\mathcal E_1$ and $\mathcal E_2$ are bigger than $\mathcal E$, then a current will always flow through the galvanometer and so no null point will ever occur.
The maximum possible potential difference across the potentiometer wire $PQ$ is $\mathcal E$.
In practice it would be less because of the drop in potential across the ammeter, the cell $B$ due to its internal resistance and the rheostat.
At balance, no current through the galvanometer $G$, the potential drop across the wire $PJ$ must equal the emf, $\mathcal E_1$ or $\mathcal E_2$, of the cell connected to the circuit.
If the potential difference across the whole wire $PQ$ is less than $\mathcal E_1$ or $\mathcal E_2$ then no such balance point can be found.
So the emf of cell $B$ must be bigger than $\mathcal E_1$ (or $\mathcal E_2$) otherwise there will be no balance point.