Eddie's Skyline is awarded for completing all 15 of Eddie's Challenges (which also unlocks Eddie Is Back in Need for Speed
) after which Eddie's car is ready to buy in your garage but Eddie will also call you and inform you that you own his car now.Eddie's car will be purchasable from your garage for the lovely price of 0.
Now once owned and driving go to any race you're comfortable with and win the event with Eddie's car, I looked for any (easy) events. I used 'In The Driver's Seat' which is just up from the garage on the map and takes about 2minutes. Eddie's car isn't bad but its also not the best.
Here's a video (Gotta love other people driving head onto you in the world)