You must tighten your mesh, i.e. to add some edge loops along the contours.
The result is already more acceptable even if you see some weird dark shadows along some edges. The subsurf modifier will polish all this.
Any way, doing some cube modeling for such a round geometrical shape is… hmmm… sub-optimal. Modeling it at an angle is even more sub-optimal. And not using a Mirror modifier is unspeakably sub-optimal. (You see what I mean.)
All you have to do is to respect the proportions. Starting from a circle seems the most logical choice in here. I used a circle with 40 vertices for the outside and 60 vertices for the middle. (Don’t ask from where I pulled these numbers… They just happen to work.) I had to rotate just a little bit the inner circle to make the “branches” straight. Then I kept only one quarter with 8 faces. That’s enough for the scale at which I worked. It doesn’t really align with the background image but the result is good IMHO.
Well, since I have no use for this blend file, before I delete it, here it is…
tf2logo.blend (555 KB)
It’s not perfect to the 5th decimal but I’d use it any way if I had to. It’s free in every way, CC0 and all. Enjoy!