Find all bounded continuous functions $f:\mathbb R\longrightarrow \mathbb R$ which satisfy the following condition: \[ f^2(x)-f^2(y)=f(x+y)f(x-y)\ \ \text{for all $x,y\in \mathbb R$}.\] Here $f^2=f\cdot f$ is the square of the function $f$ (and not the composition of $f$ with itself).