The font awesome icon set is supported if you have a plugin (or theme) that adds this font set (eg tabby responsive tabs customiser) in this case you can add an icon parameter to each tabby shortcode.
eg:
[tabby title="My Tab" icon="cog"]
This adds the classes required by font awesome which you can check by viewing the page source.
If you don’t want to use font awesome icons – eg you want to use your own custom icons, you can target the added classes with additional CSS rules to add your own icons.
so there’s no simple way of adding images next to text?
It should be simple if you can add a few lines of CSS.
The answer given in this topic may help: https://wordpress.org/support/topic/need-to-add-image-of-country-flag-next-to-each-tab-title
