Subtraction by addition

$$9-7=9-(10-3)=9+3-10=12-10=2$$

As you have asked for a "visual" explanation:

The "complement" of $7$ is the number of steps it needs to reach $10$ (that is $3$). But on the way to reach $10$, it reaches $9$ first. Thus, of the $3$ steps, $2$ steps are needed to reach $9$, and the remaining $1$ step takes $9$ to $10$. So, when you add $3$ to $9$, the first thing that happens is that $9$ itself reaches $10$ in that $1$ step, and then it goes above $10$ with the remaining $2$ steps. When you remove $10$ from this answer (by discarding the "extra $1$ on the left"), you get the $2$ steps which $7$ actually takes to reach $9$.

It was amusing to explain this, but I agree with Thomas in finding this method unnecessary and crippled.

$$9-7 = 10-8 = 11-9 = 12 - 10$$