Sending a custom email

I'm trying to send a custom email to our site admin
when a user encounters an error on the signup.php form.

My custom code is in the error.inc.html file. It sends an email
just fine (using phpmail), so it's working up to that point.

However...

I also want to include the form data entered by the user
in the body of the email. But when I include the standard
variables in my code, no data is shown in the email message.

For example, here's some code in the error.inc.html file:

First Name: {$name_f}
Last Name: {$name_l}
Email: {$email}

... which is shown in the email as:

First Name:
Last Name:
Email:

What do I need to do to get the variables to show in
the email? I've got a feeling I need to format the
variables in a different way, or use some "include"
or "require" command.

While I'm at it, I'd also like to show the actual error
message in the email too. I believe the variable is
$error or {e}

Is that possible?

I'm obviously not a coding pro.

Any suggestions?

~ Quickdraw

Does anyone have any expertise on the above challenge?

Show us what you know ;-)