Differential amplifier exercise problem
i think you mistake, as the DC voltage of Vi1=Vi2=-0.5Volt, your circuit is symmetric, the DC current of each side of the circuit is 0.25mA.
so you can calculate RE:

RE=0.5-VBE-RE*(0.5mA)=-15V

RE=27.6 K ohm

re = 1/gm = VT/IC = 0.1Kohm

iac = (0.5.sinw)/(1/gm + 2.RE)=(0.5 Volt)/(55.2Kohm + 0.1Kohm)= 9 mA

RC.iac = 1 Volt

RC = (1 Volt) / (9mA) = 0.11 Kohm