If you use the great backup script from ghettoVCB you have an option to email the logs. However the port is not open on the ESX firewall so
1. Create a text doc called smtp.xml and add the following.
SMTP_Outbound outbound tcp dst 25 true false
2. Upload this file to /etc/vmware/firewall/
3. Run esxcli network firewall refresh on the ESX device.