1. **State the problem:**
We have a two-digit number whose digits sum to 11.
2. **Define variables:**
Let the tens digit of the original number be $x$ and the units digit be $z$.
3. **Write the sum of digits equation:**
$$x + z = 11$$
4. **Express the original number:**
The original number is $$10x + z$$.
5. **Square the original number:**
$$ (10x + z)^2 $$
6. **Form the new number by interchanging digits:**
The new number formed by interchanging digits is $$10y + x$$, where $y$ is the tens digit of the new number.
7. **Given condition:**
Subtracting 45 from the square of the original number gives the new number:
$$ (10x + z)^2 - 45 = 10y + x $$
8. **Write the equation in terms of $y$:**
$$ y = \frac{(10x + z)^2 - 45 - x}{10} $$
This is the required equation in $y$.
**Note:** We do not need to convert this into quadratic form.
Digits Equation
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