How can text be justified on both the left and right sides of a line in Word?

Yes!

1. Make sure you can see the ruler at the top of the page
2. Click in the ruler to place a tab marker and then drag it over to the right hand side of your page.
3. Now double click on the marker and change the alignment to right.
4. Now when you press TAB while typing on that line, instead of just indenting your text a bit, you can type text aligned to the right of the page.

This is accomplished with tabs. The tab stops that show in the ruler at the top of the page determine not just the position of the tab, but also how the text will be aligned relative to that marker.

You can quickly set tabs by clicking the tab selector at the left end of the ruler until it displays the type of tab that you want and then clicking the ruler at the location you want.

The various types of tab alignment have intuitive symbols:

Source

In your case, you position Left and Right tab stops where you want them and insert a tab character between the portions of text that will be left- and right-aligned.