There is another way around to root your X10 eclair direct from the X10 itself.
The apk name is z4root. You can download here and will be availabe soon in the market.
After download, just install the apk (or put it in your phone first or install using adb if you’ve download it from computer) and click root button.
The developer said it should be 100% safe since nothing on disk is changed beside the root binaries. If something goes wrong, just reboot your X10.
Update: download the z4root 1.2.1 (re-root and un-root methods are availble)
Source : XDA