Add Search to top Nav/Menu Area

I would like to add the search box to the right end of the top menu area. I think I could get it in the menu but I’d like it set off right justified on that same horizontal area. Any tips/suggestions would be appreciated.

I am sure this would involve both editing the header.php & some CSS and I am ok with that. I have tried but it always put the seach on new line in that area and I’d like it on the same line as the menu, but right justified.

Thanks
Andy