Kindly refer to the attachment. I have mentioned my query in it.

Dear Student,

No, its not wrong. Since E2 is short-circuited you can take that out from the circuit since it will play no role anymore. So the current in the circuit will be E1/r1+R.
This current should be greater than that provided by E2 i.e E2/r2. So as to increase the current through R E1/r1+R > E2/r2
So current through E1 and E2 basically will be same and not different since they are in series. But when short circuited you can conside E2 as non-existent.