T = mg - mf for f

T = mg - mf for f

Subtract mg from each side:
T - mg = mg - mg - mf

Cancel the mg on the right side and we get:
T - mg = -mf

Multiply each side by -1:
-(T - mg) = -(-mf)
mg - T = mf

Now Divide each side by m to isolate f:
(mg - T)/m = mf/m

Cancel the m on the right side and we get:
f = (mg - T)/m