Living in stuttgart

Try www.numbeo.com for living costs.

For a single person it is a decent middle-class salary but don't expect to live like a king or save half of your pay. The biggest cost is usually housing and the market is very tight in Stuttgart thus not cheap. Desirability of a location can depend on the proximity to where you work or to good public transportation lines for commuting. It is especially difficult as a foreigner to rent an apartment so it can be a great help if your employer or co-workers can give some assistance in finding something.

thanks for the replies @TominStuttgart and @stumpy

I don't want to live like king . I'm planning to come with the wife, she won't be able to find a job soon. So that offer is not enough for 2 people?  Also is it harder than finding an apartment in Berlin

The offered pay (€45k/year) is on the low side for a software engineering job.
However, it is sufficiently above the minimum income for a two-person-family and thus you should be able to survive quite well if you forgo expensive hobbies, travel and other luxuries.