SamCute, did you - putting END_DATE into your example - mean that this is a column constraint? I forgot what DB you use; perhaps there you can do it. But, in Oracle you'd get "ORA-02438: Column check constraint cannot reference other columns" error which means that check constraint that references other column must be a table constraint.
Finally, the syntax would be
alter table mytable
add constraint ch_date_interval
check (end_date > start_date);