Hi Carel,
 
The theme you are using for your website is forcing all the images in the page to have the property “display: block” (which is quite unusual).
 
The quickest solution is to add this lines to your stylesheet (via Admin panel: Appearance -> Editor -> edit the style.css):
.cn-modern .cn-wrapper li a span img {

    display: inline !important;
    padding-top: 20px;
}
 
The display property will prevent the general rule in your style to be applied to the menu.
The padding added is to fix a little bit the overall result given the settings of your current theme. It is the pad between text and the icons themselves. Feel free to tweak it and play with it until you are happy with the results (try 10px, or try 30 px, etc).
 
Please, if you have any doubt about how to apply this changes here we are 🙂 And please tell us of you manage to get the menu working as you want.
 
Best wishes