In=
ct = 0.0183; cf = 0.01; pu = 120.15; ku = 4.5; kRu = 0.0274;
eq1 = pu == 1/3*(1/TpE + Tu/(ue*(ct + cf)));
eq2 = ku == 4*pu^2*(ct + cf)*TpE - Tu/ue;
eq3 = kRu == 2*pu^3*(ct + cf)*TpE*TEu;
Solve[{eq1, eq2, eq3}]//Quiet
Out=
{{TEu -> 0.000100002, TpE -> 0.00279097,
Tu -> 0.0608804 ue}, {TEu -> 0.0000449806, TpE -> 0.00620494,
Tu -> 5.63985 ue}}