I assume that you mean "is homologous to" by "encodes the same protein as". Identical ("same") proteins should be fairly trivial to identify using a tool such as tblastx.
You should probably not use E-value for this. E-value is similar to a p-value, in that it represents some aspect of the data (in this case a sequence and a database) compared to some null hypothesis (meaning in this case statistics on the database). Therefore, it depends both on the specifics of the data and the hypothesis, and there is no universal threshold that will work across all sequences and all databases. (See discussion of the meaning of e-value.)
E-value does not in any way represent the content of the sequence or its relationship to a sequence in the database. You could have E-values close to zero or E-values > 10 for a perfect sequence match or a very loose sequence match, depending on the input sequence and the database.
However, BLAST output does include other information that might be helpful. You could (for example) look at the length of the alignment and the number of mismatches/identities in the alignment. This will give you a pretty good guess at how similar the two sequences are; unless they are very divergent you would expect them to align across most of the length with somewhat high protein identity or similarity (>25% probably?). This process will still not work 100% of the time, but I think it is closer to your intent than any given approach involving E-values.