"I understand that my linux architecture is considered to be "little endian" while Solaris is "big endian", but I'm not sure what that really means. "
Here are two explanations of what little endian and big endian mean.
The other thing that you need to know is the format of the fields in the records on the binary data file that was written on a 64-bit Solaris box. Is each field a two byte binary number, a four byte binary number, or what? Do you have any floating point numbers which is a whole different kettle of fish?
Once you know the format of the Solaris fields you can probably convert each field by using modulo arithmetic. Or, alternatively, you could use Google to find a Fortran endian conversion routine.
Be prepared. Create a LifeBoat CD.