Unfortunately, Google does not allow users to send texts through Gmail. Sending texts from Gmail was a service that was available up until April 1st, 2014, but it was discontinued and therefore is no longer possible.
Google's email service Gmail used to allow users to send and receive SMS messages between a computer and a phone. Users were able to click on "compose" in Gmail and enter the desired recipient's phone number and a specific tag for whichever cell phone carrier the recipient had, then write messages that would appear on the cell phone as text messages. The messages on the cell phone could be replied to, and they would be sent back to the original sender's email account. Similarly, users could use the "chat" feature to send and receive text messages even quicker.
While this service was very popular among Gmail users, it was discontinued in April 2014 for unknown reasons. There has been plenty of backlash towards Google by users to bring back text messaging, but Google has not responded. Users who want to communicate with cell phone recipients from their Google accounts are still able to use a service called Google Voice. Google Voice allows users to send and receive voice messages between a computer and a cell phone.