email to text

You really shouldn't try to answer questions when it is obvious that you are not very knowledgeable on the topic.  First of all it is, "are you on the Mobile Network or WiFi”, not “are you on DATA or WiFi."  Second, this has zero bearing on the problem.  A text message via email is not restricted by the type of network being used to send/receive, either network should work.  The only real possibility is if T-Mobile is blocking text messages originating as an email.  And then there is the whole thing about my statement above "when I am browsing the internet from a PC and want to send a particular link to”  which my PC has no "Mobile Network, or in your terms DATA".  You'll never get a job with T-Mobile unless it is selling phones where you have to have zero knowledge of your product