Not with HTML alone. The best HTML can do is what you described: Open the installed mail client and have the user send the email.
If you want to send the email with no user interaction, you'll have to use some type of Server-Side language such as ASP or PHP or Coldfusion, and use the language's mail functions to send it.
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Ignorance is not necessarily Bliss, case in point:
Unknown has caused an Unknown Error on Unknown and must be shutdown to prevent damage to Unknown.