Retrieve alert error description text via SQL Server Agent
Tokens may be what you're looking for:


  SQL Server Agent token replacement is simple and efficient: SQL Server
  Agent replaces an exact literal string value for the token. All tokens
  are case-sensitive. Your job steps must take this into account and
  correctly quote the tokens you use or convert the replacement string
  to the correct data type.


Using $(ESCAPE_SQUOTE(A-MSG)) should allow you to access the description from an error message when the agent job is triggered by an alert.