You can indeed. In your messaging app, press the menu option, then settings, then go all the way down on the options page and select ringtone (it only affects the text messaging). Select the ringtone for your text message notification and press OK. Then back out of the options page. You've just now set your "ringtone" for your text message.
On your email app (I'm assuming it's the Gmail app), press menu, then SETTINGS, then slide down the options page all the way to the bottom and select "ringtone" (this will only affect your email). Select "SILENT" ringtone, then OK. Back all the way out of the options page. You've just now set your "SILENT" ringtone for your email.
My phone is set up exactly as you have described. When I receive text message, it plays a ringtone I created for text messages and when I receive email, it plays another "ringtone" to let me know someone loves me enough to SPAM me. LOL.