10、Given the function $f(x)=\frac{9 \sin x \cos x}{(1+\sin x)(1+\cos x)}\left(x \in\left(0, \frac{\pi}{2}\right)\right)$. If $f\left(x_{0}\right) \in N$, then $x_{0}$ is called an "ideal number". Find all the ideal numbers.
10. Analysis: Let $\sin x + \cos x = t, t \in (1, \sqrt{2})$, then $\sin x \cdot \cos x = \frac{t^2 - 1}{2}$, i.e., $f(t) = \frac{9 \cdot (t - 1)}{t + 1} = 9 - \frac{18}{t + 1} \in (0, 27 - 18 \sqrt{2})$. Therefore, if $x_0$ is an ideal number, then $f(x_0) = 1$, at this time $t = \frac{5}{4}$, i.e., $\sin 2x_0 = \frac{9}{16}$, hence $x_0 = \frac{1}{2} \arcsin \frac{9}{16}$ or $\frac{\pi}{2} - \frac{1}{2} \arcsin \frac{9}{16}$.