I lost my wallet identifier and mnemonic. What I only have is my Bitcoin receiving address,
1EAd1Qua6fzyenPeSMRxYcpbcKgYUBpxQ7. I also lost the "Welcome to my wallet..." message in my e-mail. What do I do now? Please help, my bicoins are inside!
If you neither have the mnemonic, the identifier, or the wallet file, there is probably nothing that can be done to restore your wallet.
Especially, the receiving address is not sufficient to restore your wallet. Otherwise, any other user could claim your wallet as it is public knowledge. Clearly, that would not be secure.
As Murch said, the mere knowledge of an address is not sufficient to be able to spend bitcoins from that address. If it was you'd be able to spend bitcoins from the recipient's address after you've paid them.
In this case, you mention you lose a "Welcome to my wallet..." message. If you remember this email, you might remember what third party sent it. From the way you present it, it seems likely that third party generated the address and private keys for you, so might still be able to get them to you if you contact them. However, this is only a long shot, and if they indeed do, be prepared to give copious evidence of your claim to this wallet, as easy recovery of a wallet's private keys would make this vulnerable to social engineering.
If this doesn't work, then short of brute forcing (impossible for all intents and purposes), there is nothing you can do to recover those bitcoins.