I can't find anything in the documentation of SOAP API which would discuss how to create an Email using a Template. It is possible from the UI, but no mention how to do it using SOAP.
2 Answers
You cannot do this with standard functionallity in the SOAP-Api. You can however create a global APEX class with a method sending your email using your template. Your method will need to be a "webservice static".
You will get a specific WSDL for your APEX-class that you need to use to be able to call your method. You need to set SessionHeaders for this service, just like you do when logging in to the regular SOAP-Api. Use the same SessionId and Endpoint URL you got from that login to this new service.
You can find more of the details on the link: https://developer.salesforce.com/page/Apex_Web_Services_and_Callouts
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1While your answer might be correct, and workable, I've just discovered SendGrid. Cheaper, faster, and many times easier to use. I was up and running and doing exactly what I needed within an hour. ExactTarget will no longer be part of my solution.– DarekCommented Jun 1, 2014 at 15:13
If you're using .Net you can use my Nuget package ExactTarget.EmailFromTemplate.
Source code here: https://github.com/alwynlombaard/exacttarget-email-from-template-creator
Basically I'm building up the SOAP envelope, you can see how I do it in the source if you want to do something similar in another language.