Let, circle is $x^2+y^2+2gx+2fy+C=0$

and the length of the tangent from $\left(7,15\right)$ as $l$ units, then
$1+9+2g+6f+C=2$ … $\left(1\right)$
$9+49+6g+14f+C=18$ … $\left(2\right)$
$49+225+14g+30f+C=l^2$ … $\left(3\right)$
Now, equation $2\left(1\right)+\left(3\right)$ implies
$2+18+49+225+18g+42f+3C=4+l^2$
$\Rightarrow 69+225+3\left(6g+14f+C\right)=4+l^2$
$\Rightarrow 69+225+3\left(18-58\right)=4+l^2$ (from $\left(2\right)$)
$\Rightarrow l^2=225+69-4-120$
$\Rightarrow l^2=170\Rightarrow \left|l\right|=\sqrt{170}$
$\Rightarrow$ length of the tangent from $R$ is $\sqrt{170}$ units