How to calculate cost of equity?
Your formula is wrong. The derivation for the cost of equity $r_E$ is actually:

$r_A = r_D(1-t)\frac{D}{V}+r_E \frac{E}{V}\\
r_E \frac{E}{V} = r_A -  r_D(1-t)\frac{D}{V}\\
r_E = r_A \frac{V}{E} -  r_D(1-t)\frac{D}{V} \times\frac{V}{E}\\
\mathbf{r_E = r_A \frac{V}{E} -  r_D(1-t)\frac{D}{E}}$

Since $\frac{D}{V}=\frac{D}{D+E}=0.09091$ when $r_A=0.1941$, then $E=10$ which means $D=0.10E=1$, making $V=D+E=11$ for use in the above.

$r_E = 0.180 \times\frac{11}{10}-0.06(1-0.35)\times 0.10 = 0.1941$