I=mne/me+nr make m subject of the formula

as written, nothing can be done, since mne/me = n

and all the m's go away.
So, I'll go with
I = mne/(me+nr)
I(me+nr) = mne
Ime + Inr = mne
Ime-mne = -Inr
m(Ie-ne) = -Inr
m = Inr/(ne-Ie)