e=(p-w)/(t(p-w))=1/t because p-w cancels out and et=1, provided p≠w.
Multiply through by pt-wt:
ept-ewt=p-w
w(1-et)=p(1-et).
So w=p assuming et≠1. Note that this solution renders the original equation undefinable.
ALTERNATIVE SOLUTION (alternative interpretation)
e=p-(w/pt)-wt
(w/pt)+wt=(p-e)
w((1/pt)+t)=(p-e)
Multiply through by pt: w(1+pt^2)=pt(p-e)
w=pt(p-e)/(1+pt^2)