How to create a separate theme for a custom page?
To create a custom template for node/123, copy your theme's default page.tpl.php to a file named page--node--123.tpl.php (D7) in your theme's or subtheme's templates/ directory, and then edit it to do any customization.

To do custom theming, add custom classes where you need them in the custom template, and then add the CSS to style those classes.

Btw.: I usually do this by creating a sub-theme, to avoid any customization from being overwritten when the super-theme is upgraded.

PS: If your page really has the path example/123, the name of the template overide file should be page--example--123.tpl.php

Remember to clear the cache after doing this.    Until you do, your override will not be visible.