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It is possible, it's just going to be a hassle.

UPDATE: before you try this method, please have a look at Steven's answer.

You're going to need the testdisk package, a lot of disk space and a lot of time.

PhotoRec, a part of TestDisk, can recover files from almost any disc. PhotoRec does support finding .tex files.

First, install testdisk by running

yum install testdisk

note: You're going to need a lot of free space on another drive, where you can save recovered files.

Recover all the deleted files on your disc by running photorec on the free space of the disc.

sudo photorec

and follow the instructions... ( remember not to save the files to the same disc you are recovering from )

After the process has completed, all the recovered files should be in one directory, where you should run:

find -name '*.tex' > filelist

This will output a list of files that might be the one you lost. You will have to check all of them, as the filenames will be lost.

Many text editors keep backup files. If you are really lucky, there might be something like yourfile.tex~ including a previous version of your file.

There are other data recovery tools and the most effective are foremost, photorec, scalpel and magic rescue. (I'm assuming that the 'grep' trick told here is not enough) Here you can find some tutorials about how to use them:

http://www.howtogeek.com/howto/15761/recover-data-like-a-forensics-expert-using-an-ubuntu-live-cd/

https://help.ubuntu.com/community/DataRecovery

In any case I'd stop working on the device being used as soon as possible to avoid any disk writes, and boot into a dedicated recovery OS, like SystemRescueCd, which is a Live-CD so you can mount your disk read-only in order to prevent further data loss.

Those distros include a lot of recovery tools mentioned by others, and you can install most missing.

I always tend to have a CD with a recent version of SystemRescueCd in my external USB reader, just in case.

NOTE: I added this answer regarding some other question about deleted database files (MySQL server) which was closed and pointed to this one. I believe it can be useful in some other similar situations too (as far as some process still holds the file descriptors open).

If your process is still runnig then you can find your files in /proc/<pid>fd/ and just copy them. Send SIGSTOP first to the process group. Copy the files. Build new instance on side and keep this one stopped or kill -9 it and put the files back on their places. InnoDB will recover by its own when run but if there was some MyISAM than you'll have to do this manually.

I had accidentally deleted my sqlite db file.

What I did to find out the file was,

Opened the location /proc/ in a file browser and searched for the deleted sqlite db file over there.

I found out that file in a search result. Copied that file from there to my old place.

I had the same problem two years ago and I tried a lot of programs, like debugfs, photorec, ext3grep and extundelete. ext3grep was the best program to recover files. The syntax is very easy:

ext3grep image.img --restore-all

or:

ext3grep /dev/sda3 --restore-all --after date -d '2015-01-01 00:00:00' '+%s' --before `date -d ‘2015-01-02 00:00:00’ ‘+%s’

This video is a mini tutorial that can help you.

If you have no backup a 3rd party Disk Recovery Tool might recover some or all of the data but you must stop using the machine now.
The trashed files are now available for your system to overwrite them. Once they are overwritten it's prohibitively expensive to recover the data.
I've had success using uflysoft data recovery(there are other Mac OS data recover applications)- you must have a "recovery drive" (not your main drive or drive you a scavenging from) on which to save the recovered data. You boot from the Data Recovery disk (system)