How are the scaling parameters included (extracted from) an essential matrix?
The Essential matrix is defined only up to scale, so you cannot extract scale from it. In other words, if you multiply $t$ and all the 3D world points in your scene by a constant factor, the essential matrix will be the same.

If you have to get the scale, then you need some additional information. Either you need to have an object of a known size in the scene, or you need some other sensor that tells you what the translation between the cameras is (e.g. GPS, odometer, or IMU). Here is an example where you get scale from a sphere of a known radius that happens to be in the scene.