Copying Text Titles from one Image to another in 2018

I am going to take a stab at this, providing I understand correctly what it is you are trying to achieve.

You are adding a layer of text to a PSD file and you wish to then add that same layer to countless PSD files at will, right ?

I am not sure about how to do this to a whole batch; but, here is how I would do them one-by-one.

You can save a text layer on top of a solid layer as a PSD file and then use that text layer over and over; keep it in a dedicated folder and you will always have it.

To use it on other PSD files/layer stacks, load the desired text file in Elements, along with the files you wish to add it to.

Do Window > Images > Tile

This will put all the open images visible side-by-side.

Click on your text image; it should become active in the layer stack.

Mouse over to the text layer and "grab" it;  hold and drag it on top of another image while holding the Shift key - holding the Shift key makes it land centered so you don't have to do that later.

Now, you do not have to go back to your text layer --- just grab > drag > and drop the text layer from image to image until you have got them all.

I hope I am making sense.

Hi popcorn,
Just in case you use Elements+, please, try the following:
- Open all the photos in PSE Editor
- Open E+ "Scripts" dialog (fig. 1)
- Choose "Misc. Utilities" category (fig. 2)
- Run "Meta Stamp" script (fig. 3)
- In the dialog that opens, enable "Custom Text" option and enter the desired title text (fig. 4)
- Disable "file name" and other unnecessary options 
- Specify the title position, font color, and other settings (fig. 5)
- Check "Stamp all open images" gadget (fig. 6)
- Click "Run"

Hi popcorn,
The text is added as a separate Type layer.
So, yes, you can edit it as needed.