1. **Problem Statement:** Find two numbers given their sum and difference. Given: - Sum of two numbers $A + B = 7\,849$ - Difference of two numbers $A - B = 1\,073$ 2. **Formula and Explanation:** To find the two numbers, use the system of equations: $$\begin{cases} A + B = S \\ A - B = D \end{cases}$$ where $S$ is the sum and $D$ is the difference. Add the two equations: $$ (A + B) + (A - B) = S + D \Rightarrow 2A = S + D $$ Solve for $A$: $$ A = \frac{S + D}{2} $$ Subtract the second equation from the first: $$ (A + B) - (A - B) = S - D \Rightarrow 2B = S - D $$ Solve for $B$: $$ B = \frac{S - D}{2} $$ 3. **Calculation:** Substitute $S = 7\,849$ and $D = 1\,073$: $$ A = \frac{7\,849 + 1\,073}{2} = \frac{8\,922}{2} = 4\,461 $$ $$ B = \frac{7\,849 - 1\,073}{2} = \frac{6\,776}{2} = 3\,388 $$ 4. **Verification:** Check sum: $$ 4\,461 + 3\,388 = 7\,849 $$ Check difference: $$ 4\,461 - 3\,388 = 1\,073 $$ 5. **Answer:** The two numbers are: $$ A = 4\,461 $$ $$ B = 3\,388 $$ Note: The numbers 9,776 and 7,961 mentioned in the prompt do not satisfy the given sum and difference conditions, so the correct solution is as above.