The pattern with single-syllable words ending in -e is that the final e lengthens the vowel sound. So ban becomes bane, can becomes cane, etc. But then what happens to that final e when we start to add other endings?
The general rule is that if the added bit starts with a consonant then there is no problem. So safe gives rise to safety, stale gives rise to staleness, advertise gives rise to advertisement. But there is a difficulty with judge, which in British English gives rise to judgement, and in American English to judgment. Australian English, sandwiched between the other two, can do both, although we prefer judgement.
When the added part starts with a vowel, things understandably become more difficult. Mostly the rule is that the -e is dropped before the other ending goes on. So race becomes raced and racing, not raceed and raceing. But with endings like -able we like to be able to see the base word, so slice becomes sliceable, and manage becomes manageable. Words that end in -ie change the ie to y before adding -ing. So die gives rise to dying, lie to lying.
Consider these examples:
advertisement: This word comes from the word advertise, although there is a change in the sound. This should remind you not to leave out the e before the final ment. The spelling rule is that words ending in e keep their e when followed by a suffix that begins with a consonant. Rap it out as ad + ver + tise + ment.
argument: This word is formed from the verb argue. Words formed from argue do not follow the rule which says that words that end with e keep the e before a suffix starting with a consonant. So in argument and arguable the e from argue has been left out. There’s no argument about that!
indicator: When the -or ending is added to indicate, the -e is dropped, following the rule that when a suffix starting with a vowel is added, you lose the -e.
senate: A member of a senate is called a senator, following the rule that the final e is dropped when adding something to a word.
storage: You will have no trouble with the spelling of this word if you see that it is made up of store (with the e dropped) and the suffix -age (used in nouns referring to a state or condition).