Not possible for most feasible purposes (not saying not possible at all). It won't be easy. Unless you have a comprehensive understanding of x86 assembly and know exactly which bytes of the xls file were affected. And that data hasn't been replaced by new files on the hard disk. Either that or using a drive saver program/service.
What kind of data was it? Not to sound harsh but I find it hard to believe it's not replaceable somehow...? If you didn't reboot your PC you could also try dumping your memory to get the part of it that didn't get replaced. You could also try this program called Restoration (freeware). Not sure if you can get it to get 'part' of a file. There are services like Drive Savers (
www.drivesavers.com). Not sure what they could do for you as they mostly recover drives from head crashes. No idea, but if it's that serious your time would be well spent investigating them. I'm thinking you overwrote it with blank cells so chance of recovery is almost nil, unfortunately. Most of these programs and services recover files, not data from within files. The data MAY be lurking on your hard disk but the complexity of finding it and retrieving it isn't even funny. Anyway,
http://www.snapfiles.com/get/restoration.html
http://www.drivesavers.com/index.html
But again I'm in serious doubt these programs and services can retrieve lost (let alone overwritten) data from within files. Only the files themselves. The way they work if they look for data that don't exist in the master boot record (partition table and file table). Somehow they get the filename of the data and present it to you...I'm unsure of the whole process. What I do know is, one time I tried recovering a file (an exe) and it didn't run correctly, so it must have been stray data from somewhere else on the hard drive. There's a reason there's government policies for erasing data throughly. That reason being that data can be restored even though it's been replaced. Next time you have serious data just make sure you make a backup copy or 500 (on different media besides your hard disk). Good luck...
Also there COULD be extra files where the .xls file resided like backup files...depending on your options in Microsoft Excel. Like if the workbook was named book1.xls, there could be a book1.[something else] file(s). If there is, make a copy of the file(s) so they don't get overwritten. You might be able to use them to get the data some how.