This is indeed a very good introduction to Lambert function.
Sooner or later, you will learn that any equation which can write or rewrite $$A+Bx+C\log(D+Ex)=0$$ has solution(s) which espress(es) in terms of this function.
In the case of natural logarithms, using the steps shown in Ross Millikan's answer, you would end with $$x=12+\frac{1}{\log_e (2)}W\left(\frac{e^2 \log_e (2)}{4096}\right)$$
Assuming logarithms in base $2$ as the numbers suggest, then, as Ross Millikan answered, $$x=12+\frac{1}{\log_e (2)}W\left(\frac{\log_e (2)}{1024}\right)$$
Assuming logarithms in base $10$, $$x=12+\frac{1}{\log_e (2)}W\left(\frac{25 \log_e (2)}{1024}\right)$$
Now, since the argument is quite small, you can approximate the value of $W(t)$ using the expansion $$W(t)=t-t^2+\frac{3 }{2}t^3-\frac{8 }{3}t^4+O\left(t^5\right)$$ or, better, using Padé approximants such as $$W(t)=\frac{t }{1+t }$$
$$W(t)=\frac{t+\frac{4}{3} t^2}{1+\frac{7 }{3}t+\frac{5 }{6}t^2 }$$