There are regional and phone network restrictions for Skype. They may well be different for Nokia phones than Android phones, and your friend may not be on the same phone network as you.
There (is now) one official Skype app in the Play Store, and one I know of that isn't in Play Store:
Skype on Three- Three UK customers only, follow directions on the linked page to get it
Skype - requires Android 2.1+, works on all phone networks (outside of the US) where your phone network allows it.
The above options for finding Skype in the Play Store only work if your country has its own Play Store, if your country currently uses the "Rest of the World" Store, then you won't be able to find Skype. According to Skype's FAQ, if this is the case then you should go to GetJar.com and download Skype from there.
Assuming you're not in a country/network that's blocking Skype then your problem may be the Android OS version on your phone, I think most Xperia x10's are still running Android 1.6 and the normal Skype app requires that you be running Android 2.1 or newer.
I think most countries have an Eclair (Android 2.1) upgrade for X10's, check what Android version your phone is running, and then find out if an upgrade is available.