How can I restore a deleted file that I should not have deleted? I used titanium backup to delete something I shouldn't have deleted and than I factory reseted my phone and now I can't log in with my Google accounts ,can anybody please tell me what I have got to install for this ?
There's a free app on the play store called Undeleter that may help once you can root your device again. It sounds like you erased your Google play services, Google framework, and possibly your Google+ /data when you wiped it. Which is normal. Titanium backup's /data is stored on your sd card, or even internally sometimes in a different directory that is most often protected by root even when you factory reset it.

Boot into recovery using the button press sequence, factory wipe it, and the Dalvik cache, adb push a stockROM.zip file from the manufacturer or just Google search it.

Reboot back to recovery and flash the Gapps file, which also is a .zip file, for your specific Android device, and reboot one more time. 

Wait five or ten minutes while it loads the first time. Mine have taken 30 minutes before just after flashing a new ROM, so just have patience. Then you can link it to Wi-Fi and reload your Google account info.