18. Let $a=\log _{5}\left(3^{x}+4^{x}\right), b=\log _{4}\left(5^{x}-3^{x}\right)$, if $a \geqslant b$, try to compare the size of $a$ and $x$.

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18. From the given conditions, we have
\[
\left\{\begin{array}{l}
3^{x}+4^{x}=5^{a} \\
5^{x}-3^{x}=4^{b}
\end{array}\right.
\]

Adding the two equations, we get
\[
4^{x}+5^{x}=4^{b}+5^{a}.
\]

Since the function \( f(x)=4^{x}+5^{x} \) is monotonically increasing on \(\mathbf{R}\), and \( a \geqslant b \), we have \( 4^{a} \geqslant 4^{b} \). Therefore, from (1) we get
\[
f(x) \leqslant 4^{a}+5^{a}=f(a),
\]

which implies \( x \leqslant a \).
Note: Similarly, it can be shown that \( b \leqslant x \).