There are a couple of fairly simple AutoHotkey scripts given as answers to related Software Recommendations questions:
Note that neither of these quite corresponds to the existing left and right arrow combos. The factory Windows behavior is that pressing Win+← followed by Win+→ restores the active window to what it was before you pressed anything (which may just be a floating window that doesn't touch any edges of the screen). But these scripts do not remember the original window position or size. In principle, it should be possible to modify the scripts so that they do remember the state of each window before tiling, but that's beyond the scope of this answer and is left as an exercise for the reader.
I think it's worth mentioning that you can achieve the tiling you're looking for without additional software, but it's not as convenient as you'd like.
How-To Geek explains that you can open Task Manager, select the (in your case two) applications that you want to tile, right-click any of them, and choose "Tile Horizontally". (You can tile any number of applications horizontally or vertically with this method.)