Circuit analysis with dependent current source and tricky voltage source
Put the bottom common node at ground; then \$V_b \equiv V_{R_2}\$. The circuit becomes:







simulate this circuit &ndash; Schematic created using CircuitLab

KVL says: \$V_b=V_0+R_EI_E\$ where \$I_E=I_B+(1+\beta)I_B=I_B(1+\beta)\$ and \$I_B=I_{R_1}-I_{R_2}=\frac{Vcc-V_b}{R_1}-\frac{V_b}{R_2} \$. Putting it all together with a bit of trivial maths readily gives (I'll skip steps):
$$V_b+V_b(1/R_1+1/R_2)R_E(1+\beta)=V_0+\frac{V_{cc}R_E(1+\beta)}{R_1} \\V_b\left( \frac{R_1R_2+(R_1+R_2)R_e(1+\beta)}{R_1R_2}\right)=V_0+\frac{V_{cc}R_E(1+\beta)}{R_1}$$
solve for \$V_b\$ and you're done.