Hmm...I'm not sure what's available in the Philippines. Find a substrate that you can get really damp without water actually running out of it. I would place it around the stray egg, without actually touching it (since it might be too wet), and maybe place a plastic tub upside down over the whole arrangement to hold in humidity and heat (kind of like a humid hide for the egg). You could also try packing the substrate around the egg loosely, forming a kind fo nest, but you'll need to judge how wet it is as to whether it's safe to do direct contact (this would impart the most moisture, though).
How do the other eggs look in comparison?