There has been a recent discussion about exporting from Lightroom to Elements:
Export FROM Lightroom to Elements
I'll try to detail the procedure by describing the differences and similarities between both softwares.
1 - Both are using catalogs to store the information about each of your media files. The information from your camera (date, shutter speed...) as well as your tags, captions or notes are stored in the catalog. The catalogs keeps those informations (metadata) as well as the location (drive, folder) where the image itself is stored.
2 - You could have various catalogs from Elements or Lightroom pointing to the same media files (no duplication of the media files themselves) but what you do in a catalog is ignored by other catalogs, even in the same software.
3 - The catalogs from Lightroom and Elements are different, they are not compatible. Adobe provides a tool to 'convert' an Elements catalog into the Lightroom format, but nothing for converting from Lightroom to Elements.
4 - When people want to recover the above metadata (exif data, tags...) for another software (based or not on catalogs) the general workflow is to 'write metadata to tags'. You can do that either from Lightroom or Elements. Your tags and captions will be recovered, but you'll lose a number of info which can only be stored in catalogs, like albums, collections, stacks, version sets, creations, tags and collections hierarchies...)
5 - In practice, you use the Lightroom commands to 'write metadata to files' to copy the metadata (tags, captions, notes, ratings...) to the files themselves. Then you use the 'Import' function of Elements to populate its catalog from the files themselves. That's about all, and that's not different from a migration from Lightroom to any third-party software.
6 - What is different in the case of Lightroom and Elements is the management of raw files. Lightroom and the Adobe Camera Raw (ACR) plugin in Photoshop and Elements share the same way to convert raw files and to edit those non-destructively. In short, that means that the editing 'recipe' for the images is stored in the catalog and in the metadata header of the files. When you import the files in Elements, you recover not only the tags and captions, but the editing 'recipe'. If you have saved most of your files in Lightroom with various edits without creating output copies, the editing work is lost for third-party softwares. It's mostly recovered in Elements. That's where xmp files are used. When the editing history in Lightroom has to be written to files, it's not possible to overwrite or update raw files, so small xmp text files are created along the original raw file to store that history.