currently in number theory is there a method to solve for integer solutions to equations like $2^x+3^y=9^z+8^w+8^t$?
For example, $2^{13}+3^6=9^3+8^4+8^4$. (obtained using computer brute force)
In general, is there a way to solve for ${A_1}^{x_1}+{A_2}^{x_2}+\ldots+{A_n}^{x_n}={B_1}^{y_1}+{B_2}^{y_2}+\ldots+{B_m}^{y_n}$ or is it out of scope of the current number theory methods? ($A_i$ and $B_i$ are the given numbers, want to solve for $x_i$ and $y_i$)
Sincere thanks for help!