Can the equation $\ln(x)+ 1- x^2=0$ be solved without the Lambert W function ? (I didn't study Lambert W yet).
By inspection I can see that $x=1$ is a solution. Are there other solutions? And is there a systematic way to find them?
Note: I asked this similar question concerning $\ln(x)-1+x^2$, however, the answer there cannot be used for the function here.