You can't edit text in a JPEG. It's a plain bitmapped graphic: just a series of pixels. The computer has no way of knowing that there's text in the image, much less what that text actually says. Most likely, your friend wasn't actually working with a JPEG. There is some software which can perform OCR on a JPEG to extract text, but these programs create text files for you to edit; they can't write the text back to the original file.
I'm sorry that I can't help more than this; I'm afraid you'll have to type it out again. If I may ask, though, why do you use a JPEG for your resume? Why not use a PDF, or some other vector-based format? The file should be smaller, it would certainly look better when printed, and software which can display PDFs is almost as universal as software which can display JPEGs.