If you refer to Oracle's Certification Matrix you will see that both Oracle 22.214.171.124 and 10gR2 are certified and supported on the Solaris 10 operating system. This gives you some options in terms of whether you want to first upgrade the database or the operating system.
Since you are moving to completely new hardware, you can choose to migrate the 9.2 database to the new server and then upgrade it to 10gR2, or you could perform the upgrade at the same time as the migration.
Because this is an Oracle E-Business Suite database, I will assume that it is a large database and that export and import is not feasible. Review the Oracle Database 10g Release 2 (10.2) Upgrade Guide for options on how to migrate a database to 10gR2. I would also urge you to consult the required Oracle E-Business Suite documentation to ensure that whatever upgrade option you choose is supported.
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