Suppose $n>2$. By Fermat's Last Theorem, we know that $a^{n}+b^{n}=c^{n}$ has no non-trivial solutions. Can we quantify it more?

More specifically, given $a,b,c,n\in\mathbb{N}$ with $n>2$ and $a^{n}+b^{n}\neq c^{n}$, can we prove lower bounds on $\lvert a^{n}+b^{n}-c^{n}\rvert$ in terms of $a,b,c,n$? Also assume that $a,b,c$ are distinct.