I lost my original 1200d charger (LC-E10E) and by mistake ordered an LP-E8E charger. Will it charge my battery pack?
It might, but the dangers involved with having a charger that doesn't fit the contacts on the battery you have would make me recommend you not try. Shorting across the contacts could be a fire hazard, and mis-matching contacts would mean the battery won't charge properly. The fact that the LP-E10 battery has flat contacts and the charger has pins, while the LP-E8 has thin blades as contacts and the charger has slots basically means your battery simply doesn't fit correctly in the LP-E8 charger.
I'd recommend returning the wrong charger and getting the right one.