Sender Unit Issues?

My 2005 explorer was working fine this morning. I filled it up at lunch time only to notice that my gauge still showed empty. I also have a digital gas gauge that shows how many miles to empty I have left. After my initial freak out of thinking somehow I hadn't actually just put 60 dollars of gas in my car, I noticed the gauge slowly start to rise. However, the digital mileage read out continues to drop. What is this issue? How do I fix it? And can I do it myself? All help greatly appreciated

Matt