Maths
posted by Beth .
Rearrange for T and J;
n=(2J+1)exp((BJ(J+1))/(KT))
where B and K are constants

Here's how you would do it for T.
ln n = ln (2J+1) BJ(J+1)/kT
ln [n/(2J+1)] = BJ(J+1)/kT
kT = BJ(J+1)/ln[n/(2J+1)]
Now divide both sides by k
Work similarly to solve for J 
I understand how you do it for T, but since there is more than one J, I don't understand how you make J the subject.