Summary Fields/Capture change in value

Hello -

I need different values to appear when adding a record, editing, and viewing. I know we can do this with multiple fields and form rules but I need an extra step for editing a record. When the user first edits a record one field would show (a summary field from another table), when they change a value on the form while editing I then need to show to a field that holds that summary value + the changed value. Would it be possible to do this using a single formula field?

For example:
Summary = 50, X = 10

When adding a new record I would see 60

When viewing the record I would see 50

When editing the record I would, at first see 50
If I change x from 10 to 15 I then want to see Summary + (abs(10-15)) = 55

1. Currently, when i edit and change the value from 10 to 15, this would show me 65. Is there a way to capture the difference between the original X value and the new value entered?
2. Is there a way to add a condition to a formula field to show different fields based on when the user is adding, editing or viewing?
(possibly adding some form of condition based on the url? like "?a=API_GenAddRecordForm" is used when a url formula field is used to add a new record)

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Thanks in advance,
Jennifer Paschal
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