hi.........the full solution is given below............. i think in this ques. e1 and e2 are equal dnoted as e oterwise in the relation there is also term of e1 and e2 exist..
I (currnt) = 2e/r1+r2+R
V (volt) =e -- (I) r1
we know that voltmeter is giving reading zero then
0 = e --(2e/r1+r2+R) r1
by solvng
**** R =r1--r2 ****
here R is external resistance.......