Let's say I have a total bankroll of $1,000.
For a coin toss of 52% and even money back, the bet should be...
$$\begin{align} (0.52 * 2 - 1) * $1,000 = 0.04 * $1,000 = $40 \end{align}$$
What would the formula look like for a 7% chance of 10 times the bet?
I am not a mathematician, so please be gentle with the explanation/formula.
You will get a negative number because this is a losing bet and you want to take the other side. It looks like you get your stake back when you win as you are defining it, so your formula gives $(0.07\cdot 10-1)\cdot 1000=-300$ so you should bet $300$ on the other side. Read starting with "If the edge is negative" on Wikipedia.