I have two images of equal dimensions that I'd like to be able to have displayed on the same line. How can I do this using the 2010 version of Word?

I'm not sure why you're having a problem. I'll assume that you are not putting the images in text boxes.

Word's default is to format inserted pictures as "in line with text." If you insert one image, then a second, with no keystrokes in between, the images will both sit on the same line as long as their combined width fits within the page margins. If not, the second will jump to a second line. Sizing down one or both images will resolve the problem.

You will want to right click on your images and check the text wrapping. Make sure that it is inline. Also, check your margins. You may think that your images should fit on the line, but they may be flowing into the margin. I hope this helps.