The differential is inside the housing that you removed. When you look inside the housing you will see a pinion gear and a crown gear attached to the differential case. Limited slip differential (LSD), sometimes called positraction. Limited slip differentials use various mechanisms to allow normal differential action when going around turns. When a wheel slips, they allow more torque to be transferred to the non-slipping wheel. By filling them with different weight oils you can tune them to transfer power differently to the front and rear drivetrain, and wheels. You have to remove the diff from the housing. Then you open it by removing the crown gear. If you have a manual it will give you an exploded view. You would disassemble it according to the instructions. Clean it very well, then fill it with the weght oil of your choice before you closeit up. I usually fill them about 85% full. That is just the way I was shown. I am sure others may do differently. If you study the manual for a minute it will show you how to do this procedure.