How to recover iTunes songs from old computer?

I have been searching around forums and haven't found a problem with my case. I manually added all my songs to my iPhone from my old computer on iTunes. I sold the computer and wiped it clean. With my new computer, I clicked the manually add option again, and forgot to read the fine print. Now, my entire library on my iPhone is gone, is there any way to recover the songs I had from my old computer? I tried restore to no avail.

Sorry. If the phone has forgotten them, and the computer doesn't have them, and Apple doesn't have any record of you purchasing them, then they're gone. Only the songs tied to your Apple ID are available from the cloud.

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