In a bipolar transistor at room temperature if the emitter current is doubled the voltage its junction across base-emitter (for η = 1): 

In a BJT emitter current is doubled and one has to find the base emitter voltage, so we consider the p-n junction formed by emitter and base. The junction current is given by

Given the current is doubled 

So, 

or 

Since, 

Then 

or, 

Taking η =1

V_be2 - V_be1 = 1 × 0.026 × 0.693

= 18 mV