Is it possible to solve for two unknowns from one equation?

The answer to the original question 'Is it possible to solve for two variables related by single equation' is, YES!

Here is an example. Solve for two unknown real numbers $x$ and $y$ given a single equation $$x+\sqrt{y-1}=\sqrt[4]{1-y}$$ The only real solutions are $x=0,y=1$

---

Solution As $x,y$ are real numbers, either $y-1\ge0$ or $1-y \le0.$

Assume that $y$ is strictly greater than $1$, then the LHS of the equation is a real number, whereas, the RHS will have non-zero complex part. A similar argument is also true when the value of $y$ is strictly less than $1$. Therefore, $y = 1$ is the only possible solution. Indeed, $x = 1$ and $y = 0$, is a solution, and the only one.

This may be considered as a hack, since apart from the equation, we have two constraints, i.e., $x$ and $y$ are Real. There are complex solutions to the equation.

Not uniquely. You can solve for $x$ with $x = 32 - 3y$, and if you choose any $y$, you'll have an $x$ so the corresponding $(x, y)$ pair is a solution. Conversely, you can solve for y in terms of $x$, and then use (any? or just integer $x$ so that $y$ is an integer -- you filed this under "diophantine equations") $x$ choices to get $y$s for $(x, y)$ solution pairs.