How to solve $a(\exp\left(\frac{b}{x}\right)-1)=c(\exp\left(\frac{b}{x-d}\right)-1)$ for $x$? where $a,b,c,d$ can be treated as constants.
This problem is a simplified version of dividing the Planck's equations of $2$ different conditions. $$B=\frac{2hc^2}{(\lambda^5)\left(\exp\left(\frac{hc}{\lambda kT}\right)-1\right)}$$ I want to find the emissivity of some material, and I think I have to find the temperature of as least $1$ condition for calculation (the temperature difference between $2$ conditions is known). I tried to solve for $T$, but I found it cannot be solved normally. Some suggested numerical methods but I don't really know how to do it. Please help.