Example in .vimrc
let @e='02f{lyt}:!makeex ^R"^M:tabe ex/^R"/^R"-sol.tex^M:vsplit ex/^R"/^R".tex^M'
The problem is, ^R (<Ctrl-r>) and ^M (<CR>) are single special characters. You have to enter them bei preceeding them with <Ctrl-v>.
Or simply paste them in Insert-Mode with C-r C-r q (provided the macro is stored in register q)
Record your macro q and then show it with :reg q. Replace all special chars.