Please write clearly I have posted this twice already and ne

Please write clearly, I have posted this twice already and neither time has it been neat enough to read. Please mention any substitutions prior to doing them. Thank you. Will rate legible and understandable answers.

Solution

Let the current flowing in R4 be I1 and in the R1 arm be I2. So the current in the R5 branch will be I2 - I1 all the currents are assumed to be in clockwise direction

Hence writing kirchoff\'s law.

E1 + RI2 + 2R(I2 - I1) - I2R = 0

And for the upper loop

E2 - I1R + 2R (I2-I1) -I1R = 0

Hence I2 =I1 - E1/2R

Putting it in eq 2

I1 = E2 - E1 /2R