Which Macs support HDMI with ethernet?
Please explain: are you attempting to update your TV's firmware? If so, check the TV's manual - I'm pretty sure it's done by loading from your Macbook to a USB drive. HDMI over ethernet is a system built to provide  a digital television signal over two cat5 cables. It requires extra hardware on each end, and is quite likely not what you are looking for. 
If all you need is that internet connection, go to the "Sharing" preferences and turn on internet sharing by sharing your WIFI connection and checking the Ethernet box. Now connect the laptop and TV's ethernet ports.