Another good reason to change/amend default ports for UI and MS is sSetting up TLS, especially in a dual mode (ie, leaving both http and https access), That is why you can find additional information about port configuration in documentation pages dedicated to TLS configuration.
Both types of ports, http and https, are situated nearby to each other. So, by tracking https port changes, you can identify the location of http ports.
There are actually three different ways to change these ports, CWC, manual and config-file-based.
To change a port of Edge UI manually
https://community.apigee.com/questions/22482/how-to-change-the-port-of-apigee-enterprise-ui-fro-1.html
or in the documentation
http://docs.apigee.com/private-cloud/latest/setting-port-number-edge-ui
To change a port of Ege UI TLS using config file
http://docs.apigee.com/private-cloud/latest/configuring-ssl-management-ui
To change Management Server TLS port
http://docs.apigee.com/private-cloud/latest/configuring-ssl-management-api
To change Management Server http Port
For your specific question, as you are talking about port 8080, you want to change a port of Management Server not Edge UI.
Using CWC, you need to override value set by an install process
/opt/apigee/customer/application/management-server.properties
conf_webserver_http.port=8080
For details on CWC, see
http://docs.apigee.com/private-cloud/latest/how-configure-edge