Oh ok so you are using the "underline" button in the text editor i guess.
Well try this: Create a "text format" of type "character". Choose an underline style for the text format. There are 2 available. Then you can apply that character text format to words in a text in the texteditor via the "formats" dropdown. Maybe that is already enough. If you want to further customise the underline, please use the textformat's HTML class to do your css styling. In "Textformats" every format's html classname is listed. It is basically just the name of the format with an underscore _ before it.
It can be really hard with css to define the space between a word and an underline. You can try to change the line-height property to affect that space.