Short answer is 'No'.
Explanation is the fact that XE 10g has 1 GB RAM limit, therefore no benefit and sense to make 64-bit version of XE 10g.
However you can run XE on 64-bit Linux anyway - one easy way to obtain this is to install a 32-bit system, complete with all libraries and apps but without a kernel, into a chroot.
Hmmm, we need a 64bit version not to have more access to RAM but simply to be able to do a simple instalation and run a demo in a 64 bit machine (which nowdays are very common). Obviously we need the other versions of the DB in order to run largar databases. The point of having a simple, low-footprint DB for demos and development trainning and students is negated if we need to install a whole set of additional libraries and chroot the thing. We need a 64 bit version, with the current RAM limitations.
I have been running XE on 64bit Ubuntu machines for long time. There are couple of 32bit library dependencies such as 32bit libXm.so and that is all there is to it to run XE under 64bit. Besides, if you want to use it for demonstrations and don't want to install additional 32bit libraries under a 64bit Linux OS then you can always use a VM such as Oracle's VirtualBox running 32bit version of anything (OS) you want with XE on it. So, what is the big deal ;) - I don't think you will ever see a "10gR2" compatible XE in 64bit.