1. **State the problem:** Calculate the sum of the two numbers: $1183375846816782 + 112910770486564738901982734656478392019827364563728910$. 2. **Formula used:** Addition of two numbers is done by summing their digits starting from the rightmost digit, carrying over when the sum exceeds 9. 3. **Perform the addition:** Since the second number is much larger, the sum will be close to the second number plus the first. 4. **Add the numbers:** $$1183375846816782 + 112910770486564738901982734656478392019827364563728910 = 112910770486564738903165110503295174939025738209545692$$ 5. **Explanation:** We simply add the two numbers digit by digit, carrying over as needed. The first number is much smaller, so it increases the second number slightly. **Final answer:** $$112910770486564738903165110503295174939025738209545692$$