There *is* an IE10, but it's very old and unsupported. From your remark about Cortana I understand you're using Windows 10. Windows 10 has IE11. lets you add Google search. And Tools>Manage Addons from the menu bar lets you set it as default (but it doesn't have Autocomplete like Bing, or like Google in Firefox). That missing autocomplete might be a good argument to not use IE11, but switch to Firefox. It's free and IE11 is nearly deprecated.

If you don't see a menu bar, you can enable that via a right click somewhere in the line with the tabs. But surely you, as an enthousiast user of IE (there aren't many left), knew that.

By the way, to disable Cortana this is the way: "To Turn off Cortana completely on Windows 10 Pro press the “Start” button and search for and open “Edit group policy“. Next, go to “Computer Configuration > Administrative Templates > Windows Components > Search” and find and open “Allow Cortana“. Click “Disabled“, and press “OK“"
The group policy editor is only available in Windows 10 Pro. If you happen to have Windows 10 Home, there surely is way to do the same with regedit, but I didn't search for it.