Gorell Window Help
Sure, the "T" shaped base of the 58-182 should just slide into the channel from the opening at the edges. If that channel is sealed, which is the case on some windows, then you have to make an opening yourself. The video below will show you how this can be done.
Oh gosh, I'm sorry for misunderstanding. I see what you mean now.
The method of putting a sash back in the window varies depending on the kind of balances you have. It sounds like you might have tilt windows, but that is just a guess; usually when you tilt a window into the house for removal, you engage parts known as "pivot lock shoes." These lock in place and keep the springs from shooting up like you describe.
If your springs are shooting up anyway then it sounds like the pivot shoes aren't functioning properly, or maybe just didn't engage in the first place. It's also possible you have a totally different system altogether, I admit that this is just an educated guess.
I can tell you exactly what you need to do to make your life easier, but I will require photos of the springs in question and whatever hardware connects to them.
https://www.swisco.com/Pivot-Lock-Coil-Housing/pd/Tilt-Window-Replacement-Pivot-Lock-Shoes/15-087 this looks like I remember
https://www.swisco.com/Pivot-Bar-3-inch/pd/Tilt-Window-Replacement-Sash-Pivot-Bars/26-063 I think this was the one
Aha, that's all I need to know. So, replacing sashes with this kind of pivot shoe can be pretty frustrating since the cams that take the pivot shoe are closed. That doesn't allow you to simply lift the pivot bars up and out of place.
There is a way to do this more easily, but it takes some finesses. What you have to do is twist the sash as you tilt it in, which results in one pivot shoe being higher in the track than its partner on the opposite side. That angle allows the pivot bars to slip right out of the cam without much fuss, and then right back in when you're ready to put the balances back in place.
I know that may be hard to visualize. If you watch the video below, you can see my old pal Mike do this on the sample sash we use during the tutorial. The spring hardware used on this window is a little different but the method of removing the sash (and putting it back in) is exactly the same as on your window.