1. **State the problem:** We have a two-digit number with tens digit $t$ and units digit $u$. When this number and its reverse are added, the sum is 143. 2. **Define variables:** Let the units digit be $u$. The tens digit $t$ is given by the rule: $t = u^2 - 7$. 3. **Express the numbers:** The original number is $10t + u$. 4. **Express the reversed number:** The reversed number is $10u + t$. 5. **Write the sum equation:** $$ (10t + u) + (10u + t) = 143 $$ 6. **Simplify the sum:** $$ 10t + u + 10u + t = 143 $$ $$ 11t + 11u = 143 $$ 7. **Divide both sides by 11:** $$ \cancel{11}t + \cancel{11}u = \frac{143}{\cancel{11}} $$ $$ t + u = 13 $$ 8. **Substitute $t = u^2 - 7$ into the equation:** $$ (u^2 - 7) + u = 13 $$ 9. **Final equation in $u$ (not quadratic form):** $$ u^2 - 7 + u = 13 $$ This is the required equation in $u$.