Solution:
The voltage at the base of transistor Q3 is
Assuming that the transistor Q3 has the same characteristics as diode D1 and D2 that is VD = VBE3, then

Practically we take RE = 240 Ω.

Practically we take R2 = 3.6 kΩ.

To obtain the differential gain of 60, the required value of the collector resistor is

The following fig. 7 shows the dual input, balanced output differential amplifier with the designed component values as RC = 1K, RE = 240 Ω, and R2 = 3.6KΩ.